| In quantum mechanics,the reality of a physical observable and the unitary dynamics for a quantum system rely on the fundamental postulate of the Hermiticity of the associated operators.However,a non-Hermitian Hamiltonian with parity-time(PT)symmetry may also possess a real energy spectrum.Although this concept was initially developed and extended in the field of quantum mechanics,its application in this field is fundamentally limited because quantum mechanical operators are inherently Hermitian.However,this is not the case in optics,in which PT symmetry can be introduced by providing gain and loss under specific conditions to photonic systems.Due to their high degree of flexibility and controllability,gainloss-balanced optical systems provide a versatile platform to exploit the fundamental nature of the non-Hermitian PT-symmetric quantum mechanics in experiment.Thus far,a number of PT-symmetry-related phenomena has been observed,including spontaneous PT-symmetry breaking,unidirectional invisibility,etc.The experimental results also prompted researchers to further explore the PT symmetric quantum theory and prove the topologically protected bound states of photonic PT-symmetric crystals and a non-Hermitian two-dimensional topological phase transition.On the other hand,advancements in graphene-related research have provided new ideas for two-dimensional space exploration,and honeycomb photonic lattices can achieve properties that are not possible in electronic graphene systems.This thesis is in such a research background,in this thesis,the energy spectrum properties of two dimensional PT symmetric non-Hermitian quantum systems are studied theoretically.The basic idea of this thesis is as follows:Firstly,we theoretically investigate the band structure of the PT-symmetric non-Hermitian bilayer honeycomb photonic lattice(BHPL)by considering the co-existence of onsite energy detuning and PT-symmetric imaginary potentials.By introducing PT-symmetric complex potentials on the sublattices to clarify its special band structure change.The numerical results show that such complex potentials can efficiently modify the energy spectrum of the BHPL,including various energy degeneracies and deformation of the band structure.As the onsiteenergy detuning is also taken into account,its induced particle-hole symmetry breaking causes the band structure to undergo more abundant transformations.The above results indicate that PT symmetry causes the system’s energy spectra to display salient features,Notable phenomena manifest with the various energy-band degeneracies and deformation of the band structure in the vicinity of the Dirac point.Also,the strain plays nontrivial roles in modifying the band structure and PT-symmetry breaking.The strain is an important mechanism to weaken PTsymmetry breaking,under a certain condition,PT-symmetry breaking can be restored.Secondly,due to the abundant energy properties of the BHPL,its corresponding ribbon geometries certainly exhibit intricate energy properties,dependent on their edges.There are two edges for the existence of honeycomb lattice strips:zigzag and armchair edges.While zigzag edges support localized states,armchair edges do not.These edge states occur at zero energy,the same as the Fermi level of undoped graphene,meaning that low energy properties may be substantially altered by their presence.Therefore,we select the Zigzag edge structure of the band,and further discuss the band structure of the double-layer honeycomb photonic lattice band under the condition of inter-layer bias voltage and virtual potential energy coexisting.The results show that the topological properties of the system can be changed by introducing the virtual potential in the case of inter-layer bias voltage,and the original edge states can be changed by adjusting the virtual potential contributes a new state to the system and can form a state isolated from the bulk.The results show that the PT symmetric imaginary potentials and onsite energy detuning can significantly regulate the energy spectrum properties of the system,including energy degeneracy and deformation.At the same time,in the presence of interlayer bias,the PT-symmetric virtual potential energy is able to change the topological properties of the corresponding strip structure and is accompanied by the appearance of new edge states.All the above results indicate that PT symmetric imaginary potentials play an important role in regulating the band structure of the two-layer photonic lattice.It provides a theoretical reference for further study on the effect of PT symmetry on the energy spectrum properties of two-dimensional system. |
